I set this sim up to try to understand standard deviation better.
A $1000 bet with a 3.19% advantage played 1.23% of the time will result in +$0.39 win per round on average. (1000 * 0.0319 * 0.0123 = $0.39)
(99% of the hands are not bet so that's why the "per round" average falls such a small number.)
The average win per round is $0.39 but the standard deviation per round is $127.48 per round.
How can the standard deviation be 325x larger than the average win?
You only make a bet 1.23% of rounds. So 98.77 rounds out of 100 your bet and EV is 0. The other 1.23% you bet $1,000 and either win or lose $1000, push, win $1500 with a BJ or get a double and/or splits and can push or win or lose even more money.
EV = 1000*.0123*.0319 = $0.39237
SD is the square root of (sum of the squares of the round EV's divided by the number of rounds). If wins and losses where all $1,000 the SD would be slightly over $100/round but there are larger wins and losses due to BJ's doubles and splits so it works out to a slightly higher number of $127.48/round.
For SD if you assume you push about 8% of all bets made you would have 1.13 resolved bets per 100 rounds. SD would be sqrt($1,130,000/100 rounds) or sqrt($11,300) = $106.30/round. Like I said with higher payouts for BJ's, doubles, and splits the actual SD would be slightly higher. I have no problem with the $127.48/round SD. The issue is sitting out or pushing about 99 out of every 100 rounds causes EV/round to plummet so the relationship between SD and EV changes dramatically. As you divide by smaller and smaller numbers (SD/EV) the quotient becomes larger and larger. When you get to dividing by fractions less than 1, like $.39, rather than the quotient being less than the dividend when dividing, the quotient is more than the dividend. In this case about 2.56 times the dividend.
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